The varying interpretations of quantum probability governing quantum measurements are significantly reflected in divergent opinions on the foundations of statistics, including ensemble-frequency theory, propensity theory, and subjective degrees of reasonable belief. Although it has been suggested that a series of progressively sophisticated tests using artificial intelligence could yield increasingly significant experimental data to constrain potential resolutions to the measurement problem, no feasible experimental designs have yet been proposed. In this work, we utilize advanced deep learning technology to develop a novel experimental framework that integrates neural network-based artificial intelligence into a Bell test. This framework challenges the implicit assumptions underlying Bell tests. We demonstrate our framework through a simulation and introduce three new metric-morphing polygons, averaged Shannon entropy, and probability density map-to analyze the results. This approach enables us to determine whether quantum probability aligns with any one of these three interpretations or a hybrid of them.
{"title":"Exploring quantum probability interpretations through artificial intelligence","authors":"Jinjun Zeng, Xiao Zhang","doi":"arxiv-2409.04690","DOIUrl":"https://doi.org/arxiv-2409.04690","url":null,"abstract":"The varying interpretations of quantum probability governing quantum\u0000measurements are significantly reflected in divergent opinions on the\u0000foundations of statistics, including ensemble-frequency theory, propensity\u0000theory, and subjective degrees of reasonable belief. Although it has been\u0000suggested that a series of progressively sophisticated tests using artificial\u0000intelligence could yield increasingly significant experimental data to\u0000constrain potential resolutions to the measurement problem, no feasible\u0000experimental designs have yet been proposed. In this work, we utilize advanced\u0000deep learning technology to develop a novel experimental framework that\u0000integrates neural network-based artificial intelligence into a Bell test. This\u0000framework challenges the implicit assumptions underlying Bell tests. We\u0000demonstrate our framework through a simulation and introduce three new\u0000metric-morphing polygons, averaged Shannon entropy, and probability density\u0000map-to analyze the results. This approach enables us to determine whether\u0000quantum probability aligns with any one of these three interpretations or a\u0000hybrid of them.","PeriodicalId":501190,"journal":{"name":"arXiv - PHYS - General Physics","volume":"106 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study proposed an extension of the classical kinetic theory of gases (CKTG) that incorporates the gravitational effect on the motions of molecular particles. First, we rederived the CKTG in terms of the kinetics of constituent particles to account for the effect of accelerating particles by external gravitational fields. Consequently, we obtained an extended expression for the virial pressure in molecular dynamics under external potential fields. As indicated by our theoretical model, a pressure difference in the gravitational direction was observed in our particle collision simulations. Further analysis proved that if the external potential energy of each particle was sufficiently small (but not negligible compared to its kinetic energy), a pressure difference emerged between the walls while still maintaining the properties of equilibrium statistical mechanics, following the Maxwell--Boltzmann distribution. Notably, our model was formulated based on only fundamental knowledge of physics and is therefore suitable for educational purposes. Thus, this study obtained fundamental insights into the kinetic theory of gases under gravitational fields that are expected to be useful for both education and practical applications.
{"title":"Can the effect of an external gravitational field be incorporated in the classical kinetic theory of gases?","authors":"Satori Tsuzuki","doi":"arxiv-2409.00454","DOIUrl":"https://doi.org/arxiv-2409.00454","url":null,"abstract":"This study proposed an extension of the classical kinetic theory of gases\u0000(CKTG) that incorporates the gravitational effect on the motions of molecular\u0000particles. First, we rederived the CKTG in terms of the kinetics of constituent\u0000particles to account for the effect of accelerating particles by external\u0000gravitational fields. Consequently, we obtained an extended expression for the\u0000virial pressure in molecular dynamics under external potential fields. As\u0000indicated by our theoretical model, a pressure difference in the gravitational\u0000direction was observed in our particle collision simulations. Further analysis\u0000proved that if the external potential energy of each particle was sufficiently\u0000small (but not negligible compared to its kinetic energy), a pressure\u0000difference emerged between the walls while still maintaining the properties of\u0000equilibrium statistical mechanics, following the Maxwell--Boltzmann\u0000distribution. Notably, our model was formulated based on only fundamental\u0000knowledge of physics and is therefore suitable for educational purposes. Thus,\u0000this study obtained fundamental insights into the kinetic theory of gases under\u0000gravitational fields that are expected to be useful for both education and\u0000practical applications.","PeriodicalId":501190,"journal":{"name":"arXiv - PHYS - General Physics","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the energy-momentum characteristics of the rotating black hole - Kerr solution of general relativity in the Teleparallel Equivalent of General Relativity (TEGR) and the Symmetric Teleparallel Equivalent of General Relativity (STEGR). The previously constructed spacetime covariant and Lorentz invariant expressions for conserved Noether currents, superpotentials and charges are used. The Noether charges describe total energy, momentum or angular momentum of gravitating system depending on a choice of the displacement vector $xi$. To define covariant and invariant conserved quantities both in TEGR and in STEGR on needs to use external fields which are flat teleparallel connections. To determine the non-dynamical connections in TEGR and STEGR we use the unified ``turning off'' gravity principle. Besides, to analyse the Noether conserved quantities in these theories, we use the concept of ``gauges''. The gauge changing can affect the Noether conserved quantities. We highlight two ways to turn off gravity - by $M to 0$ and by $M to 0 , ~ a to 0$ which gives us different gauges in TEGR and STEGR. In both kind of gauges we get the expected values of black hole mass and angular momentum. Our attempts to find gauges which could lead to a correspondence to Einstein's equivalence principle for the Kerr solution where unsuccessful both in TEGR and STEGR. However, these exercises helped us to find a related gauge for the Schwarzschild solution in STEGR that is a novelty.
我们研究了广义相对论远距平行等效（Teleparallel Equivalent of GeneralRelativity，TEGR）和广义相对论对称远距平行等效（Symmetric Teleparallel Equivalent of GeneralRelativity，STEGR）中旋转黑洞-克尔解的能量-动量特性。我们使用先前构建的时空协变和洛伦兹不变表达式来表示守恒的诺特电流、超势和电荷。诺特电荷描述了引力系统的总能量、动量或角动量，这取决于位移矢量 $xi$ 的选择。为了定义 TEGR 和 STEGR 中的协变量和不变守恒量，需要使用外部场，它们是扁平的远平行连接。为了确定TEGR和STEGR中的非动力连接，我们使用了统一的 "关闭 "引力原理。此外，为了分析这些理论中的诺特守恒量，我们使用了 "量规 "的概念。量规的变化会影响诺特守恒量。我们强调了两种关闭引力的方法--通过$M to 0$ 和通过$M to 0 , ~ a to 0$，这给出了TEGR和STEGR中不同的量规。在这两种量规中，我们都得到了黑洞质量和角动量的预期值。我们试图为克尔解找到与爱因斯坦等效原理对应的量规，但在 TEGR 和 STEGR 中都没有成功。然而，这些尝试帮助我们在 STEGR 中为施瓦兹柴尔德解找到了一个新颖的相关量规。
{"title":"Mass and angular momentum for the Kerr black hole in TEGR and STEGR","authors":"E. D. Emtsova, A. N. Petrov, A. V. Toporensky","doi":"arxiv-2409.10529","DOIUrl":"https://doi.org/arxiv-2409.10529","url":null,"abstract":"We study the energy-momentum characteristics of the rotating black hole -\u0000Kerr solution of general relativity in the Teleparallel Equivalent of General\u0000Relativity (TEGR) and the Symmetric Teleparallel Equivalent of General\u0000Relativity (STEGR). The previously constructed spacetime covariant and Lorentz\u0000invariant expressions for conserved Noether currents, superpotentials and\u0000charges are used. The Noether charges describe total energy, momentum or\u0000angular momentum of gravitating system depending on a choice of the\u0000displacement vector $xi$. To define covariant and invariant conserved\u0000quantities both in TEGR and in STEGR on needs to use external fields which are\u0000flat teleparallel connections. To determine the non-dynamical connections in\u0000TEGR and STEGR we use the unified ``turning off'' gravity principle. Besides,\u0000to analyse the Noether conserved quantities in these theories, we use the\u0000concept of ``gauges''. The gauge changing can affect the Noether conserved\u0000quantities. We highlight two ways to turn off gravity - by $M to 0$ and by $M\u0000to 0 , ~ a to 0$ which gives us different gauges in TEGR and STEGR. In both\u0000kind of gauges we get the expected values of black hole mass and angular\u0000momentum. Our attempts to find gauges which could lead to a correspondence to\u0000Einstein's equivalence principle for the Kerr solution where unsuccessful both\u0000in TEGR and STEGR. However, these exercises helped us to find a related gauge\u0000for the Schwarzschild solution in STEGR that is a novelty.","PeriodicalId":501190,"journal":{"name":"arXiv - PHYS - General Physics","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the recently presented Two-Time relativistic Bohmian Model (TTBM) is first rigorously and thoroughly summarized: definition, salient properties and observational explanations (double-slit experiment). Secondly, the theory is applied to a generic circular atomic orbit, obtaining oscillations of the electron in the new time dimension, {tau} , that demonstrate the static nature of the orbitals. Something very similar happens in the case of a particle in box, where {tau}-oscillations cause the particle to spread out at steady states. Some speculations about spin and astrophysical follow. Finally, strengths and pending tasks of the model are summarized.
{"title":"Two-Time Relativistic Bohmian Model of Quantum Mechanics","authors":"Giuseppe Raguní","doi":"arxiv-2409.09049","DOIUrl":"https://doi.org/arxiv-2409.09049","url":null,"abstract":"In this paper, the recently presented Two-Time relativistic Bohmian Model\u0000(TTBM) is first rigorously and thoroughly summarized: definition, salient\u0000properties and observational explanations (double-slit experiment). Secondly,\u0000the theory is applied to a generic circular atomic orbit, obtaining\u0000oscillations of the electron in the new time dimension, {tau} , that\u0000demonstrate the static nature of the orbitals. Something very similar happens\u0000in the case of a particle in box, where {tau}-oscillations cause the particle\u0000to spread out at steady states. Some speculations about spin and astrophysical\u0000follow. Finally, strengths and pending tasks of the model are summarized.","PeriodicalId":501190,"journal":{"name":"arXiv - PHYS - General Physics","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Postselection is an operation that allows the selection of specific measurement outcomes. It serves as a powerful theoretical tool for enhancing the performance of existing quantum algorithms. Despite recent developments such as time reversal in quantum measurements and IBM's mid-circuit measurements, postselection continues to face significant challenges, most notably poor, often exponential, scaling. This study investigates how Two-Way Quantum Computing (2WQC) offers potential solutions to these challenges. By introducing the concept of postparation and enabling dynamic quantum state control, 2WQC has the potential to mitigate scaling issues and improve the practicality of postselection, thereby fostering advancements in the field of quantum algorithms.
后选择是一种允许选择特定测量结果的操作。它是提高现有量子算法性能的强大理论工具。尽管量子测量中的时间逆转和 IBM 的中电路测量等技术取得了最新发展，但后选择仍然面临着重大挑战，其中最突出的是扩展性差，通常是指数级扩展。本研究探讨了双向量子计算（2WQC）如何为这些挑战提供潜在的解决方案。通过引入后处理概念并实现动态量子状态控制，2WQC 有可能缓解扩展问题并提高后选择的实用性，从而促进量子算法领域的进步。
{"title":"Optimization of Postselection in Quantum Algorithms: A Two-Way Quantum Computing Approach","authors":"Alex Linden, Betül Gül","doi":"arxiv-2409.03785","DOIUrl":"https://doi.org/arxiv-2409.03785","url":null,"abstract":"Postselection is an operation that allows the selection of specific\u0000measurement outcomes. It serves as a powerful theoretical tool for enhancing\u0000the performance of existing quantum algorithms. Despite recent developments\u0000such as time reversal in quantum measurements and IBM's mid-circuit\u0000measurements, postselection continues to face significant challenges, most\u0000notably poor, often exponential, scaling. This study investigates how Two-Way\u0000Quantum Computing (2WQC) offers potential solutions to these challenges. By\u0000introducing the concept of postparation and enabling dynamic quantum state\u0000control, 2WQC has the potential to mitigate scaling issues and improve the\u0000practicality of postselection, thereby fostering advancements in the field of\u0000quantum algorithms.","PeriodicalId":501190,"journal":{"name":"arXiv - PHYS - General Physics","volume":"171 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper explores the advanced mathematical frameworks used to analyze symmetry breaking in high-dimensional field theories, emphasizing the roles of Laurent series, residues, and winding numbers. Symmetry breaking is fundamental in various physical contexts, such as high-energy physics, condensed matter physics, and cosmology. The study addresses how these mathematical tools enable the decomposition of complex field behaviors near singularities, revealing the intricate dynamics of symmetry breaking. Laurent series facilitate the expansion of fields into manageable terms, particularly around critical points. Residues provide a direct link between local field behavior and global physical properties, playing a crucial role in effective action formulations and renormalization processes. Winding numbers offer a topological perspective, quantifying how fields wrap around singularities and identifying stable topological structures like vortices, solitons, and monopoles. Extending these methods to (3+1) dimensions highlights the complexity of symmetry breaking in higher-dimensional scenarios, where advanced group theory and topological invariants are necessary to describe non-linear interactions. The findings underscore the importance of integrating these mathematical techniques into modern theoretical physics, with potential applications in quantum gravity, string theory, and the study of topological phases of matter. Future directions include further exploration of higher-dimensional extensions and their implications for understanding the fundamental nature of symmetry, topology, and field dynamics.
{"title":"Advanced Mathematical Approaches to Symmetry Breaking in High-Dimensional Field Theories: The Roles of Laurent Series, Residues, and Winding Numbers","authors":"Wen-Xiang Chen","doi":"arxiv-2409.08294","DOIUrl":"https://doi.org/arxiv-2409.08294","url":null,"abstract":"This paper explores the advanced mathematical frameworks used to analyze\u0000symmetry breaking in high-dimensional field theories, emphasizing the roles of\u0000Laurent series, residues, and winding numbers. Symmetry breaking is fundamental\u0000in various physical contexts, such as high-energy physics, condensed matter\u0000physics, and cosmology. The study addresses how these mathematical tools enable\u0000the decomposition of complex field behaviors near singularities, revealing the\u0000intricate dynamics of symmetry breaking. Laurent series facilitate the\u0000expansion of fields into manageable terms, particularly around critical points.\u0000Residues provide a direct link between local field behavior and global physical\u0000properties, playing a crucial role in effective action formulations and\u0000renormalization processes. Winding numbers offer a topological perspective,\u0000quantifying how fields wrap around singularities and identifying stable\u0000topological structures like vortices, solitons, and monopoles. Extending these\u0000methods to (3+1) dimensions highlights the complexity of symmetry breaking in\u0000higher-dimensional scenarios, where advanced group theory and topological\u0000invariants are necessary to describe non-linear interactions. The findings\u0000underscore the importance of integrating these mathematical techniques into\u0000modern theoretical physics, with potential applications in quantum gravity,\u0000string theory, and the study of topological phases of matter. Future directions\u0000include further exploration of higher-dimensional extensions and their\u0000implications for understanding the fundamental nature of symmetry, topology,\u0000and field dynamics.","PeriodicalId":501190,"journal":{"name":"arXiv - PHYS - General Physics","volume":"198 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The maximally extended Reissner--Nordstr"{o}m (RN) spacetime with $e^2 < m^2$ can be interpreted either as an infinite chain of asymptotically flat regions connected by tunnels between timelike singularities or as a set of just one asymptotically flat region and one tunnel; the repetitions of this set in the infinite chain being identified. The second interpretation gives rise to the suspicion of acausality, i.e. the possibility of sending messages to one's own past. A numerical investigation of this problem was carried out in this paper and gave the following result. Let E be the initial point of a radial timelike future-directed ingoing geodesic G, lying halfway between the outer horizon and the image of the null infinity in the maximally extended RN spacetime. Let E$'$ be the first future copy of E. It was verified whether the turning point of G will lie to the future or to the past from the past light cone (PLC) of E$'$. In the second case the breach of causality does occur. It turned out that the acausality is present when $V_E$, the timelike coordinate of E, is negative with a sufficiently large $|V_E|$, and is absent with a sufficiently large $V_E > 0$. In between these values there exists a $widetilde{V}_E$, dependent on the initial data for the geodesic, for which the turning point lies on the PLC. So, the identification does lead to acausality. Nonradial timelike and null geodesics were also investigated, and a few hitherto unknown properties of the maximal extension were revealed. For example, the singularity arc at $r = 0$ may be convex or concave, depending on the values of $m$ and $e$.
{"title":"Causality in the maximally extended Reissner--Nordström spacetime with identifications","authors":"Andrzej Krasiński","doi":"arxiv-2409.03786","DOIUrl":"https://doi.org/arxiv-2409.03786","url":null,"abstract":"The maximally extended Reissner--Nordstr\"{o}m (RN) spacetime with $e^2 <\u0000m^2$ can be interpreted either as an infinite chain of asymptotically flat\u0000regions connected by tunnels between timelike singularities or as a set of just\u0000one asymptotically flat region and one tunnel; the repetitions of this set in\u0000the infinite chain being identified. The second interpretation gives rise to\u0000the suspicion of acausality, i.e. the possibility of sending messages to one's\u0000own past. A numerical investigation of this problem was carried out in this\u0000paper and gave the following result. Let E be the initial point of a radial\u0000timelike future-directed ingoing geodesic G, lying halfway between the outer\u0000horizon and the image of the null infinity in the maximally extended RN\u0000spacetime. Let E$'$ be the first future copy of E. It was verified whether the\u0000turning point of G will lie to the future or to the past from the past light\u0000cone (PLC) of E$'$. In the second case the breach of causality does occur. It\u0000turned out that the acausality is present when $V_E$, the timelike coordinate\u0000of E, is negative with a sufficiently large $|V_E|$, and is absent with a\u0000sufficiently large $V_E > 0$. In between these values there exists a\u0000$widetilde{V}_E$, dependent on the initial data for the geodesic, for which\u0000the turning point lies on the PLC. So, the identification does lead to\u0000acausality. Nonradial timelike and null geodesics were also investigated, and a\u0000few hitherto unknown properties of the maximal extension were revealed. For\u0000example, the singularity arc at $r = 0$ may be convex or concave, depending on\u0000the values of $m$ and $e$.","PeriodicalId":501190,"journal":{"name":"arXiv - PHYS - General Physics","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Somnath Mondal, Meraj Ali Khan, Santu Dey, Ashis Kumar Sarkar, Cenap Ozel, Alexander Pigazzini, Richard Pincak
In this paper, we aim to investigate the properties of an almost $*$-Ricci-Bourguignon soliton (almost $*-$R-B-S for short) on a Kenmotsu manifold (K-M). We start by proving that if a Kenmotsu manifold (K-M) obeys an almost $*-$R-B-S, then the manifold is $eta$-Einstein. Furthermore, we establish that if a $(kappa, -2)'$-nullity distribution, where $kappa<-1$, has an almost $*$-Ricci-Bourguignon soliton (almost $*-$R-B-S), then the manifold is Ricci flat. Moreover, we establish that if a K-M has almost $*$-Ricci-Bourguignon soliton gradient and the vector field $xi$ preserves the scalar curvature $r$, then the manifold is an Einstein manifold with a constant scalar curvature given by $r=-n(2n-1)$. Finaly, we have given en example of a almost $*-$R-B-S gradient on the Kenmotsu manifold.
{"title":"Analysis of a special type of soliton on Kenmotsu manifolds","authors":"Somnath Mondal, Meraj Ali Khan, Santu Dey, Ashis Kumar Sarkar, Cenap Ozel, Alexander Pigazzini, Richard Pincak","doi":"arxiv-2408.13288","DOIUrl":"https://doi.org/arxiv-2408.13288","url":null,"abstract":"In this paper, we aim to investigate the properties of an almost\u0000$*$-Ricci-Bourguignon soliton (almost $*-$R-B-S for short) on a Kenmotsu\u0000manifold (K-M). We start by proving that if a Kenmotsu manifold (K-M) obeys an\u0000almost $*-$R-B-S, then the manifold is $eta$-Einstein. Furthermore, we\u0000establish that if a $(kappa, -2)'$-nullity distribution, where $kappa<-1$,\u0000has an almost $*$-Ricci-Bourguignon soliton (almost $*-$R-B-S), then the\u0000manifold is Ricci flat. Moreover, we establish that if a K-M has almost\u0000$*$-Ricci-Bourguignon soliton gradient and the vector field $xi$ preserves the\u0000scalar curvature $r$, then the manifold is an Einstein manifold with a constant\u0000scalar curvature given by $r=-n(2n-1)$. Finaly, we have given en example of a\u0000almost $*-$R-B-S gradient on the Kenmotsu manifold.","PeriodicalId":501190,"journal":{"name":"arXiv - PHYS - General Physics","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In view of relations between Riemann hypothesis and quantum theory according to the Hilbert-Polya conjecture and further investigations its proof is important for quantum physics. I conjecture to prove Riemann hypothesis according to Riemann's saddle point method to derive zeta function. This is a direct method to prove Riemann hypothesis related with my previous topological approach to analytic number theory and Riemann hypothesis.
{"title":"A conjecture to prove Riemann hypothesis","authors":"F. Ghaboussi","doi":"arxiv-2408.13292","DOIUrl":"https://doi.org/arxiv-2408.13292","url":null,"abstract":"In view of relations between Riemann hypothesis and quantum theory according\u0000to the Hilbert-Polya conjecture and further investigations its proof is\u0000important for quantum physics. I conjecture to prove Riemann hypothesis\u0000according to Riemann's saddle point method to derive zeta function. This is a\u0000direct method to prove Riemann hypothesis related with my previous topological\u0000approach to analytic number theory and Riemann hypothesis.","PeriodicalId":501190,"journal":{"name":"arXiv - PHYS - General Physics","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Diego J. Cirilo-LombardoKeldysh Institute of the Russian Academy of Sciences and CONICET-UBA-INFINA, Norma G. SanchezCNRS and The Chalonge - Hector de Vega International School of Astrophysics
A new formalism is introduced describe the physical and geometric content of quantum spacetime. It is based in the Minimum Group Representation Principle. New results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space-times. Our main results here are: (i) The Berry phases for inflation, for the cosmological perturbations, and its expression in terms of observables, as the spectral scalar and tensor indices, $n_S$ an $n_T$, and their ratio $r$. The Berry phase for de Sitter inflation is imaginary, its sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) $Mp(n)$ representation for quantum de Sitter space-time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the $Mp(n)$ group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) The mean $Mp(2)$ generator values are related to the space-time topological charge. (v) The basic even and odd $n$ -sectors of the Hilbert space are intrinsic to the quantum spacetime and its discrete levels (continuum for $n rightarrow infty$) and are it entangled. (vi) The gravity or cosmological domains on one side and another of the Planck scale are entangled. Examples: The primordial quantum trans-Planckian de Sitter vacuum and the late classical gravity de Sitter vacuum today; the central quantum reqion and the external classical region of black holes. The classical and quantum dual gravity regions of the space-time are entangled. (vii) The general classical-quantum gravity duality is associated to the Metaplectic $Mp(n)$ group symmetry which provides the complete full covering of the phase space and of the quantum space-time mapped from it.
{"title":"Entanglement and Generalized Berry Geometrical Phases in Quantum Gravity","authors":"Diego J. Cirilo-LombardoKeldysh Institute of the Russian Academy of Sciences and CONICET-UBA-INFINA, Norma G. SanchezCNRS and The Chalonge - Hector de Vega International School of Astrophysics","doi":"arxiv-2408.11078","DOIUrl":"https://doi.org/arxiv-2408.11078","url":null,"abstract":"A new formalism is introduced describe the physical and geometric content of\u0000quantum spacetime. It is based in the Minimum Group Representation Principle.\u0000New results for entanglement and geometrical/topological phases are found and\u0000implemented in cosmological and black hole space-times. Our main results here\u0000are: (i) The Berry phases for inflation, for the cosmological perturbations,\u0000and its expression in terms of observables, as the spectral scalar and tensor\u0000indices, $n_S$ an $n_T$, and their ratio $r$. The Berry phase for de Sitter\u0000inflation is imaginary, its sign describing the exponential acceleration. (ii)\u0000The pure entangled states in the minimum group (metaplectic) $Mp(n)$\u0000representation for quantum de Sitter space-time and black holes are found.\u0000(iii) For entanglement, the relation between the Schmidt type representation\u0000and the physical states of the $Mp(n)$ group is found: This is a new\u0000non-diagonal coherent state representation complementary to the known Sudarshan\u0000diagonal one. (iv) The mean $Mp(2)$ generator values are related to the\u0000space-time topological charge. (v) The basic even and odd $n$ -sectors of the\u0000Hilbert space are intrinsic to the quantum spacetime and its discrete levels\u0000(continuum for $n rightarrow infty$) and are it entangled. (vi) The gravity\u0000or cosmological domains on one side and another of the Planck scale are\u0000entangled. Examples: The primordial quantum trans-Planckian de Sitter vacuum\u0000and the late classical gravity de Sitter vacuum today; the central quantum\u0000reqion and the external classical region of black holes. The classical and\u0000quantum dual gravity regions of the space-time are entangled. (vii) The general\u0000classical-quantum gravity duality is associated to the Metaplectic $Mp(n)$\u0000group symmetry which provides the complete full covering of the phase space and\u0000of the quantum space-time mapped from it.","PeriodicalId":501190,"journal":{"name":"arXiv - PHYS - General Physics","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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